HANG_GNN_robustness_260330_1.pdf

Transcript

1. 1 SOKENDAI SOKENDAI Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approach (NeurIPS 2023) の紹介 君野 史明
2. 2 SOKENDAI ⾃⼰紹介 n 名前︓君野 史明（きみの ふみあき） n 所属︓総合研究⼤学院⼤学 情報学コース D1 n 専⾨︓ グラフ対照学習 グラフ表現学習
3. 3 SOKENDAI 1. എܠͱ໰୊ઃఆ എܠ • GNN͸Ҿ༻ωοτϫʔΫɺ෼ࢠɺιʔγϟϧ ωοτϫʔΫͳͲͷάϥϑߏ଄σʔλͰߴ͍ੑ ೳΛࣔ͢ɻ • ͔͠͠߈ܸऀ͸ɺϊʔυಛ௃͚ͩͰͳ͘Το δͷ௥Ճɾ࡟আ΍ϊʔυ஫ೖʹΑͬͯ΋༧ଌΛ ่ͤΔɻ • ͜ͷͨΊɺ௨ৗͷਂ૚ֶशΑΓ΋ʮೖྗઁಈ + ߏ଄ઁಈʯͷ྆ํΛߟ͑Δඞཁ͕͋Δɻ • ຊ࿦จશମͰͷೖྗ͸ɺೖྗ: (G=(V,E),Xraw) Ͱɺग़ྗ͸ɺग़ྗ: {y^k}k=1∣V∣Ͱ͋Δɻ ຊ࿦จͷࢹ఺ • GNNΛ཭ࢄ૚ͷྻͰ͸ͳ͘ɺ࿈ଓ࣌ؒͷ graph neural flow ͱͯ͠ଊ͑Δɻ • ͜ͷ࿮૊ΈͰ͸ɺ҆ఆੑͷ֓೦Λྗֶܥཧ࿦ ͔ΒମܥతʹಋೖͰ͖Δɻ • ໰͍͸୯७Ͱ͋Δ: ʮ҆ఆͳΒؤ݈ͳͷ͔?ʯ ΋ͦ͠͏Ͱͳ͚Ε͹ɺͲͷ҆ఆੑ͕ॏཁͳͷ ͔? ຊݚڀͷग़ൃ఺: طଘݚڀͰ͸ Lyapunov ҆ఆੑ͕සൟʹ࢖ΘΕΔ͕ɺ ͦΕ͚ͩͰ͸ఢରతؤ݈ੑΛઆ໌͠੾Εͳ͍Մೳੑ͕͋Δɻ GNNͷߴੑೳͱɺఢରత߈ܸʹର͢Δ੬ऑੑ
4. 4 SOKENDAI 2. ࿦จͷத৺తͳ໰͍ ҆ఆੑͷ࠶੔ཧͱɺHamiltonian flow ͷಋೖ ໰͍A ྗֶܥͱͯ͠ͷ҆ఆੑʹ͸ෳ਺ͷ֓೦ ͕͋Δɻ GNNͷఢରతؤ݈ੑͱ࠷΋ڧ݁͘ͼͭ ͘ͷ͸ͲΕ͔ɻ ໰͍B ϊʔυಛ௃ઁಈ͚ͩͰͳ͘ɺάϥϑҐ ૬ͷઁಈ·Ͱߟ͑ΔͱɺͲͷٞ࿦͕ඞ ཁʹͳΔ͔ɻ ໰͍C ෺ཧֶ༝དྷͷอଘଇΛ՝ͨ͠ graph neural flow ͸ɺ࣮ࡍʹΑΓؤ݈ͳͷ͔ɻ ओு • ୯ͳΔ Lyapunov ҆ఆੑ͸ɺ෼ྨڥքͷอ࣋Λอূ͠ͳ͍ɻ • Hamiltonian ʹجͮ͘ΤωϧΪʔอଘܕ flow ͸ɺա౓ͳऩॖΛආ͚ɺؤ݈ੑ޲্ʹد༩͢Δɻ • ಛʹʮอଘੑ + Lyapunov ҆ఆੑʯΛ૊Έ߹Θͤͨ HANG-quad ͕ڧ͍ੑೳΛࣔ͢ɻ ߩݙ: ҆ఆੑ֓೦ͷ࠶੔ཧ / Hamiltonian-inspired GNN ͷఏҊ / ଟ༷ͳ߈ܸԼͰͷൺֱ࣮ݧ
5. 5 SOKENDAI 3. ྗֶܥͱͯ͠ͷʮ4ͭͷ҆ఆੑʯ ຊ࿦จ͸҆ఆੑΛҰׅΓʹͤͣɺ໾ׂͷҟͳΔ֓೦ͱͯ͠੔ཧ͢Δ 5 BIBO ҆ఆੑ ೖྗ͕༗քͳΒग़ྗ΋༗քͰ͋Δɻಛ௃ϊϧϜͷ๫૸Λ๷͙ͱ ͍͏ɺ࠷΋جຊతͳ҆ఆੑɻ Lyapunov ҆ఆੑ ฏߧ఺ͷ͔ۙ͘Β࢝·Δيಓ͕ɺ͕࣌ؒܦͬͯ΋ฏߧ఺ͷۙ͘ ʹཹ·Δɻॳظ஋ઁಈ΁ͷ҆ఆੑɻ Structural ҆ఆੑ ॳظ஋Ͱ͸ͳ͘ྗֶܥͦͷ΋ͷʢύϥϝʔλ΍άϥϑҐ૬ʣͷ খ͞ͳมԽʹରͯ͠ɺఆੑతͳৼΔ෣͍͕อͨΕΔɻ Conservative ҆ఆੑ ෺ཧܥʹ༝དྷ͢Δอଘྔ͕࣌ؒʹԊͬͯҰఆʹอͨΕΔɻ Hamiltonian ܥͰ͸యܕతʹʮΤωϧΪʔอଘʯͱͯ͠ݱΕΔɻ ॏཁͳಡΈସ͑: ϊʔυಛ௃ͷఢରతઁಈʹ͸ BIBO / Lyapunov ͕ɺάϥϑҐ૬ઁಈʹ͸ Structural ͕ɺ ෺ཧతอଘଇʹجͮ͘ʮա౓ͳऩॖͷ཈੍ʯʹ͸ Conservative ͕ؔ܎͢Δɻ
6. 6 SOKENDAI 4. طଘͷ graph neural flow ΛͲ͏ݟΔ͔ ୅දతϞσϧΛʮ҆ఆੑʯͷ؍఺͔Β࠶഑ஔ͢Δ Ϟσϧ ߟ͑ํ ҆ఆੑͷಛ௃ ຊ࿦จͰͷධՁ GRAND ೤֦ࢄܕ BIBO/Lyapunov ͸৚݅෇͖Ͱ੒ཱ ऩॖత͗͢ΔͱΫϥε෼཭ΛଛͶ͏Δ BLEND Beltrami ֦ு GRAND ʹ͍ۙ҆ఆੑ ҐஔΤϯίʔσΟϯάΛಋೖ GraphCON ݁߹ৼಈࢠ ৚݅෇͖Ͱอଘྔ͋Γ Dirichlet energy อଘͷಛघྫ GraphBel Beltrami flow ৚݅෇͖ BIBO/Lyapunov Ґ૬ઁಈ΁ͷؤ݈ੑΛٞ࿦ ಡΈํ • ैདྷ͸ Lyapunov ҆ఆੑ͕͠͹͠͹ؤ݈ੑͷ୅ସࢦඪͱͯ͠ѻΘΕͨɻ • ͔͠͠ຊ࿦จ͸ɺอଘଇͷ༗ແΛ੾Γ෼͚Δ͜ͱͰɺΑΓઆ໌ྗͷ͋Δൺֱ࿮૊ΈΛఏࣔ͢Δɻ
7. 7 SOKENDAI 5. ͳͥ Lyapunov ҆ఆ͚ͩͰ͸ෆे෼ͳͷ͔ ʮ҆ఆ = ؤ݈ʯͱ͸ݶΒͳ͍ɺͱ͍͏൓ྫ ൓ྫͷ֩ ͢΂ͯͷيಓ͕୯Ұฏߧ఺΁ऩॖ͢Δܥ Ͱ͸ɺ ΫϥεͷҟͳΔϊʔυಛ௃͕࣌ؒͱͱ΋ ʹ͖ۙͮɺઢܗ෼ྨڥքΛ·ͨ͗΍͘͢ ͳΔɻ ͜ͷܥ͸ Lyapunov ҆ఆͰɺશيಓ͸ 0 ʹऩଋ ͢Δɻ ͔͠͠े෼௕͍࣌ؒͰ͸يಓ͕ x ࣠ํ޲ʹἧ ͍ɺඍখઁಈͰޡ෼ྨ͕ى͜Γ͏Δɻ ؚҙ 1 ॳظ஋ઁಈʹରͯ͠يಓ͕๫Εͳ͍͜ͱͱɺΫϥε෼ ཭͕อͨΕΔ͜ͱ͸ಉ͡Ͱ͸ͳ͍ɻ ؚҙ 2 Ґ૬ઁಈʹର͢Δ structural ҆ఆੑ͕͋ͬͯ΋ɺ୯Ұฏ ߧ఺΁ͷڧ͍ऩॖ͕ଓ͘ͳΒ෼ྨ͸ͳ͓੬ऑʹͳΓ͏ Δɻ ຊ࿦จͷస׵఺ ʮऩଋͤ͞ΔʯΑΓ΋ɺʮΤωϧΪʔΛอଘͭͭ͠৘ ใΛӡͿʯํ޲΁ઃܭΛ੾Γସ͑Δɻ
8. 8 SOKENDAI 6. ఏҊ๏ HANG ͷ௚؍ Hamiltonian mechanics ʹֶͿ৘ใ఻೻ ΞΠσΞ • ֤ϊʔυʹʮҐஔ qʯͱʮӡಈྔ pʯΛ༩͑ɺ άϥϑશମΛ Hamiltonian ܥͱͯ͠ਐԽͤ͞ Δɻ • q ͱ p ͸࿈ଓ࣌ؒͰಉ࣌ʹߋ৽͞Εɺ࠷ऴ࣌ ࠁ T ͷ q(T) ΛԼྲྀλεΫʹ࢖͏ɻ • ઃܭͷૂ͍͸ɺಛ௃ΛҰํ޲ʹ௵͢ͷͰ͸ͳ ͘ɺอଘଇͷԼͰදݱΛӡͿ͜ͱʹ͋Δɻ ෺ཧֶతͳൺᄻ ཻࢠܥͰ͸Ґஔͱӡಈྔ͕૬ޓ࡞༻͠ͳ ͕ΒશମͷΤωϧΪʔΛอͭɻ HANG ͸͜ΕΛάϥϑ্ͷ৘ใ఻೻΁Ҡ ͠ସ͑Δɻ ਤ: ࿦จ Fig. 2ʢHANG ͷߏ੒֓೦ਤʣ
9. 9 SOKENDAI 7. HANG ͷ਺ཧఆࣜԽ ֶज़తʹॏཁͳͷ͸ʮֶश͞ΕΔ HamiltonianʯʹΑΔ flow ͷఆٛ • ֤ϊʔυಛ௃͸ೖྗ૚Ͱ 2r ࣍ݩ΁ࣸ૾͞Εɺલ൒Λ q(0)ɺޙ൒Λ p(0) ͱͯ͠ॳظԽ͢Δɻ • άϥϑશମͷঢ়ଶ͸ (q(t), p(t)) ͱͯ͠ਐԽ͠ɺΤωϧΪʔؔ਺ Hnet ͸χϡʔϥϧωοτϫʔΫ Ͱֶश͞ΕΔɻ • ऴ୺࣌ࠁ T Ͱ͸ࣹӨ π((q(T), p(T))) = q(T) Λ༻͍ɺҐஔ੒෼͚ͩΛ࠷ऴදݱͱͯ͠ར༻͢Δɻ ϙΠϯτ 1 ResNet తͳ཭ࢄߋ৽Ͱ͸ͳ͘ɺ࿈ଓ࣌ؒͷඍ෼ํ ఔࣜͱͯ͠૚Λఆٛ͢Δɻ ϙΠϯτ 2 Hnet Λݻఆͷ෺ཧ๏ଇͰͳ͘ʮֶशՄೳͳΤωϧ Ϊʔʯͱͯ͠ஔ͘ɻ ϙΠϯτ 3 อଘଇΛར༻ͭͭ͠ɺԼྲྀλεΫʹ߹Θͤͨදݱ ֶशΛߦ͏ɻ
10. 10 SOKENDAI 8. ΤωϧΪʔอଘ͕ͳͥॏཁ͔ Theorem 2 ʹΑΔ conservative stability ܥ͕ Hamilton ͷํఔࣜʹै͏ͳΒɺશΤωϧΪʔ Hnet(q(t), p(t)) ͸࣌ؒʹԊͬͯҰ ఆʹอͨΕΔɻ ཧ࿦తؚҙ Hnet ͕༗քೖྗʹରͯ͠༗քͰ͋ Γɺ͔ͭঢ়ଶ͕ແݶେ΁ൃࢄ͢Δͱ Hnet ΋ൃࢄ͢ΔͳΒɺBIBO ҆ఆੑ ΋ಘΒΕΔɻ දݱزԿͷ௚؍ ΤωϧΪʔอଘ͸ɺ͢΂ͯͷΫϥε Λ୯Ұฏߧ఺΁ԡ͠௵͢Α͏ͳա౓ ͳऩॖͱ૬ੑ͕ѱ͍ɻΫϥε෼཭Λ อͪ΍͍͢ɻ طଘ๏ͱͷҧ͍ GraphCON ͸ಛఆ৚݅ԼͰ Dirichlet energy Λอଘ͢Δ͕ɺHANG ͸Α ΓҰൠతͳ Hamiltonian ΤωϧΪʔ อଘΛѻ͏ɻ ຊ࿦จͷϝοηʔδ: ؤ݈ੑʹޮ͘ͷ͸ʮ҆ఆʹऩଋ͢Δ͜ͱʯ͚ͩͰͳ͘ɺʮ৘ใͷΤω ϧΪʔతͳอଘߏ଄ʯΛ࣋ͭ͜ͱͰ͋Δɻ
11. 11 SOKENDAI 9. 2ͭͷมछ: HANG ͱ HANG-quad Vanilla HANG • Hnet Λ 2૚ͷ graph convolution ͔Βߏ੒ • tanh ΛڬΜͩޙʹ L2 ϊϧϜͰΤωϧΪʔΛఆٛ • conservative stability Λඋ͑Δ • ͨͩ͠Ұൠʹ͸ Lyapunov ҆ఆੑ͸࣋ͨͳ͍ HANG-quad • H = T(q,p) + U(q) ͷܗʹઃܭ • Lagrange-Dirichlet ఆཧΛ༻͍ͯ Lyapunov ҆ఆੑͷे෼৚ ݅Λಋೖ • ࣮૷Ͱ͸ U(q) ʹ sin ׆ੑԽ෇͖ GAT Λར༻ • conservative + Lyapunov ͷཱ྆Λૂ͏ Ґஔ͚ͮ: HANG ͸ʮอଘੑͷΈʯͷޮՌΛɺHANG-quad ͸ʮอଘੑ + Lyapunovʯͷ্৐ͤޮՌΛ෼཭ͯ͠ݕূ͢Δɻ อଘੑͷΈ͔ɺอଘੑ + Lyapunov ҆ఆੑ·Ͱ࣋ͨͤΔ͔
12. 12 SOKENDAI 10. ཧ࿦্ͷ੔ཧ: ͲͷϞσϧ͕Ͳͷ҆ఆੑΛ͔࣋ͭ Ϟσϧ BIBO Lyapunov Structural Conservative GRAND ˚ ˚ ˚ ˚ BLEND ˚ ˚ ˚ ˚ GraphCON ˚ º º ˚ GraphBel ˚ ˚ ˚ ˚ HANG º º º ˓ HANG-quad º ˓ º ˓ ˓: ੒ཱ ˚: ௥Ճ৚݅ͷԼͰ੒ཱ º: Ұൠʹ͸੒ཱ͠ͳ͍ • HANG ͸ʮอଘੑͷΈʯΛ७ਮʹ࣋ͭϞσϧͰ͋Γɺ࣮ݧͰ͸ͦΕ͚ͩͰ΋ߴ͍ؤ݈ੑΛࣔ͢ɻ • HANG-quad ͸ͦ͜ʹ Lyapunov ҆ఆੑΛՃ͑ɺಛʹҰ෦ͷҐ૬ઁಈͰ͞Βʹڧ͍ɻ ࿦จ Table 1 ͷཁ఺Λ೔ຊޠͰ؆ུԽ
13. 13 SOKENDAI 11. ࣮ݧઃܭ σʔληοτ Ҿ༻ωοτϫʔΫ: Cora, Citeseer, Pubmed ֶज़ωοτϫʔΫ: CoauthorCS Amazon: Computers େن໛ϕϯνϚʔΫ: ogbn-arxiv Ґ૬߈ܸධՁ: Polblogs, Pubmed ߈ܸ Graph Injection Attack (GIA): PGD, TDGIA, MetaGIA Graph Modification / Poisoning: Metattack ඇඪత߈ܸͱඪత߈ܸͷ྆ํΛධՁ ൺֱର৅ GAT, GraphSAGE, GCN Graph neural flows: GRAND, GraphBel, GraphCON ͞Βʹطଘ๷ޚ๏ Pro-GNN, RGCN, GCN-SVD ΋ൺֱ ධՁͷҙਤ͸ɺ୯ҰσʔληοτͰͷউഊͰ͸ͳ͘ɺ҆ఆੑͷҧ͍͕ʮଟ༷ͳ߈ܸ༷ࣜʯʹରͯ͠Ͳ Ε͚ͩҰ؏ͯ͠ޮ͔͘ΛݟΔ͜ͱʹ͋Δɻ ෳ਺σʔληοτɾෳ਺߈ܸɾblack-box ઃఆͰൺֱ
14. 14 SOKENDAI 12. ࣮ݧ݁Ռᶃ: ඇඪత GIA Ͱͷ୅දྫ σʔληοτ / ߈ܸ HANG HANG-quad GRAND GCN Cora / PGD 78.37 79.05 39.65 35.83 Citeseer / TDGIA 72.12 71.69 36.67 21.10 CoauthorCS / TDGIA 95.40 95.09 5.05 3.61 Pubmed / MetaGIA 87.58 87.40 44.36 40.42 ؍࡯ 1 ଟ͘ͷ৚݅Ͱ HANG / HANG-quad ͕ େ্͖͘ճΔɻಛʹ CoauthorCS Ͱ ͸͕ࠩۃ୺ʹେ͖͍ɻ ؍࡯ 2 GRAND ͸ Lyapunov ҆ఆੑΛ࣋ͪ͏ Δ͕ɺ߈ܸԼͰ͸ඞͣ͠΋ڧ͘ͳ͍ɻ ؍࡯ 3 อଘੑͷΈͷ HANG Ͱ΋े෼ʹڧ͘ɺ Hamiltonian ઃܭࣗମͷد༩͕ࣔࠦ͞ ΕΔɻ Table 2 ͔Βɺ୅දతͳ߈ܸɾσʔληοτΛൈਮ
15. 15 SOKENDAI 13. ࣮ݧ݁Ռᶄ: ඪత GIA Ͱ΋༗ޮ͔ 15 ৚݅ HANG HANG-quad GraphCON GRAND GCN / SAGE Computers / PGD 90.83 87.53 74.01 65.75 17.80 / 18.33 Computers / MetaGIA 90.73 89.32 87.95 81.85 36.19 / 37.51 ogbn-arxiv / TDGIA 66.36 61.93 29.77 22.69 28.43 / 4.78 ogbn-arxiv / MetaGIA 64.69 64.83 57.91 50.75 37.36 / 33.84 • ඪత߈ܸͰ΋ HANG ܥྻ͸ߴ͍ਫ४Λҡ࣋͢Δɻಛʹ Computers Ͱ͸ 90% લޙͱݦஶʹߴ͍ɻ • ogbn-arxiv Ͱ͸ HANG-quad ͕ MetaGIA Ͱᷮࠩͷ࠷ྑ஋Λࣔ͠ɺʮอଘੑ + Lyapunovʯͷ্৐ͤޮՌ ͕ݟ͑Δɻ • େن໛άϥϑͰ΋վળ͕࢒Δ఺͸ɺֶज़తʹॏཁͳ֎తଥ౰ੑͰ͋Δɻ Table 3 ͷओཁͳ਺஋
16. 16 SOKENDAI 14. ࣮ݧ݁Ռᶅ: άϥϑվมɾಟԽ߈ܸ΁ͷ଱ੑ Polblogs: վม཰্͕͕Δͱ͕֦ࠩେ 20% վม࣌ͷਫ਼౓ • HANG-quad: 89.19 • Pro-GNN: 79.56 • GRAND: 69.14 • HANG: 66.27 ͜ͷσʔληοτͰ͸ HANG-quad ͕࠷΋ڧ͘ɺLyapunov ҆ ఆੑͷ௥Ճ͕ಛʹޮ͍͍ͯΔɻ Pubmed: graph neural flow શൠ͕ڧ͍ 25% վม࣌ͷਫ਼౓ • HANG: 85.06 • HANG-quad: 84.99 • GraphCON: 86.04 • GRAND: 83.66 • Pro-GNN: 86.71 Pubmed Ͱ͸Ґ૬߈ܸͷӨڹ͕খ͘͞ɺσʔληοτґଘੑ ΋໌֬ʹ؍ଌ͞ΕΔɻ ղऍ: ͢΂ͯͷσʔληοτͰҰ༷ʹ࠷ڧͱ͍͏ΑΓɺʮอଘੑʯͱʮLyapunov ͷ௥Ճʯ͕߈ܸ༷ ࣜ΍σʔλಛੑʹԠͯ͡ޮ͖෼͚Δɻ Table 4 ͔ΒͷಡΈऔΓ
17. 17 SOKENDAI 15. Ͳ͏ղऍ͢΂͖͔: ֶज़తؚҙ ؚҙ A ҆ఆੑΛҰͭͷޠͰࡁ·ͤͯ͸͍͚ͳ͍ɻ ॳظ஋҆ఆੑɺҐ૬ઁಈ΁ͷ҆ఆੑɺอ ଘଇ͸ɺͦΕͧΕผͷ໾ׂΛ࣋ͭɻ ؚҙ B ఢରతؤ݈ੑͷ؍఺Ͱ͸ɺ୯ͳΔऩॖΑ Γ΋ʮදݱزԿΛյ͠ʹ͍͘อଘߏ଄ʯ ͕ॏཁ͔΋͠Εͳ͍ɻ ؚҙ C ෺ཧֶతؼೲόΠΞε͸આ໌Մೳੑ͚ͩ Ͱͳ͘ɺηΩϡϦςΟɾؤ݈ੑͷઃܭݪ ཧʹ΋ͳΓ͏Δɻ ʮLyapunov ҆ఆ͔ͩΒ҆શʯͰ͸ͳ͘ɺ ʮͲͷΑ͏ͳ҆ఆੑΛɺͲͷදݱزԿͷ্Ͱ࣮ݱ͍ͯ͠Δ͔ʯΛ໰͏΂͖ͩɺͱ͍͏ͷ͕ຊ ࿦จͷॏཁͳ໰୊ఏىͰ͋Δɻ ຊ࿦จ͕༩͑Δϝοηʔδ͸ʮ҆ఆੑͷ࣭ʯΛݟΑɺͱ͍͏఺ʹ͋Δ
18. 18 SOKENDAI 16. ݶքͱࠓޙͷݚڀ • ཧ࿦తʹ͸ɺconservative stability ͱ adversarial robustness ͷҼՌؔ܎͕׬શʹূ໌͞ΕͨΘ ͚Ͱ͸ͳ͘ɺओுͷҰ෦͸࣮ݧత஌ݟʹґଘ͢Δɻ • HANG / HANG-quad ͸ structural stability ΛҰൠʹ͸อূ͓ͯ͠ΒͣɺҐ૬ઁಈʹର͢Δݫີཧ ࿦͸ࠓޙͷ՝୊Ͱ͋Δɻ • ΑΓେن໛ͳάϥϑɺwhite-box ߈ܸɺҟछάϥϑ΍ϔςϩϑΟϦʔ؀ڥ΁ͷҰൠԽ΋ॏཁͰ͋ Δɻ • อଘଇ͕Ϋϥε෼཭ΛͲ͏อ࣋͢Δ͔ΛɺදݱزԿɾεϖΫτϧղੳɾҰൠԽཧ࿦ͱ઀ଓͯ͠ ཧղ͢Δ༨஍͕େ͖͍ɻ ࠓޙͷ໰͍ ʮอଘྔͷܗʯΛͲ͏ֶशͤ͞Δͱɺؤ݈ੑͱදݱྗͷ ཱ͕྆࠷΋Α͘ਐΉͷ͔ɻ ΑΓ޿͍ҙٛ ྗֶܥɾ෺ཧɾػցֶशηΩϡϦςΟͷ઀఺ͱͯ͠ɺඇ ৗʹൃలੑͷߴ͍ݚڀςʔϚͰ͋Δɻ ࿦จͷՁ஋ΛೝΊͭͭɺͲ͕͜ະղܾ͔Λԡ͑͞Δ
19. 19 SOKENDAI 17. ·ͱΊʢTakeawaysʣ • GNN ͷఢରతؤ݈ੑ͸ɺϊʔυಛ௃ઁಈ͚ͩͰͳ͘άϥϑҐ૬ઁಈ·ͰؚΊͯߟ͑ Δඞཁ͕͋Δɻ • graph neural flow ͷจ຺Ͱ͸ɺBIBOɾLyapunovɾStructuralɾConservative Λ۠ผ͠ ͯٞ࿦͢΂͖Ͱ͋Δɻ • Lyapunov ҆ఆੑ͚ͩͰ͸Ϋϥε෼཭͸कΕͣɺؤ݈ੑΛे෼ʹઆ໌Ͱ͖ͳ͍ɻ • Hamiltonian ʹجͮ͘ HANG ͸อଘଇΛಋೖ͠ɺ࣮ݧతʹߴ͍ؤ݈ੑΛࣔͨ͠ɻ • HANG-quad ͸อଘੑʹ Lyapunov ҆ఆੑΛॏͶɺҰ෦ͷվม߈ܸͰ͞Βʹڧ͍݁Ռ Λࣔͨ͠ɻ ࠷ऴϝοηʔδ: ؤ݈ͳ GNN Λઃܭ͢Δʹ͸ɺʮ҆ఆʹ͢Δʯ͚ͩͰͳ͘ʮͲΜͳอଘ ߏ଄Λ࣋ͨͤΔ͔ʯΛ໰͏ඞཁ͕͋Δɻ